In recent years, automobile technologies for the purpose of saving of energy resources and environment protection have been developed. For example, there is an idle stop system in which when a given condition (automatic stop condition) is satisfied during operation, a fuel to be supplied to an engine is cut off to lose a torque generated in an engine. The automatic stop condition is satisfied by lifting a driver's foot off an accelerator, or putting on a brake. In this idle stop system, even if a vehicle does not stop, if the automatic stop condition is satisfied, the engine is automatically stopped. Thereafter, the engine restarts when receiving a restart request from a driver, or when an engine operation is required.
As a method of restarting the engine, a method is applied in which with the use of a pinion pushing starter, a pinion of a starter is pushed to engage the pinion with a ring gear of the engine, rotation of the starter is transmitted to the engine, and the engine is rotated and started.
There has been proposed a method in which then during inertial rotation after the torque generated by the engine is lost, such a condition that the accelerator is pressed is satisfied, and the restart is requested, a motor of the starter starts to be energized to rotate the pinion, the pinion is engaged with the ring gear to start cranking by the starter when the rotational speed of the pinion is synchronized with the rotational speed of the ring gear, thereby hastening restoration of the engine rotation (Japanese Patent No. 4214401). In this Japanese Patent, a motion energy of the engine and the amount of work for preventing the motion of the engine are computed, and a future motion energy is estimated to estimate a future engine rotational speed.